相关论文: The permutation action of finite symplectic groups…

In this paper, we introduce and study the class of $\phi$-$w$-P-flat modules, which can be seen as generalizations of both $\phi$-P-flat modules and $w$-P-flat modules. In particular, we obtain that the class of $\phi$-$w$-P-flat modules is…

We consider random lower triangular matrices such that the entries on and below the diagonal are i.i.d. copies of some $\mathbb{Z}$-valued random variable. We prove that the Sylow $p$-subgroups of the cokernels of these matrices have the…

We give a classification of finite groups of symplectic birational automorphisms on a manifold of K3^[3]-type with stable and stably saturated cohomological action. We describe the group of polarized automorphisms of a smooth double…

We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…

We study the symplectic geometry of the moduli spaces of polygons in the Minkowski 3-space. These spaces naturally carry completely integrable systems with periodic flows. We extend the Gelfand-Tsetlin method to pseudo-unitary groups and…

A polysymplectic structure is a vector-valued symplectic form, that is, a closed nondegenerate 2-form with values in a vector space. We first outline the polysymplectic Hamiltonian formalism with coefficients in a vector space $V$, then…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…

We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds…

We compute the rank of the fundamental group of an arbitrary connected component of the space map(X, Y) for X and Y nilpotent CW complexes with X finite. For the general component corresponding to a homotopy class f : X --> Y, we give a…

It is shown that the set of orbits of the action of the elementary symplectic transvection group on all unimodular elements of a symplectic module over a commutative ring of characteristic not 2 is identical with the set of orbits of the…

In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group W acting on the pth graded component of its…

We consider the symplectic groupoid of pairs $(B, A)$ with $A$ real unipotent upper-triangular matrix and $B\in GL_n$ being such that $\tilde A=BAB^T$ is also a unipotent upper-triangular matrix. Fock and Chekhov defined a Poisson map of…

We investigate integral forms of simple modules of symmetric groups over fields of characteristic $0$ labelled by hook partitions. Building on work of Plesken and Craig, for every odd prime $p$, we give a set of representatives of the…

Random walk on the chambers of hyperplanes arrangements is used to define a family of card shuffling measures $H_{W,x}$ for a finite Coxeter group W and real $x \neq 0$. By algebraic group theory, there is a map from the semisimple orbits…

We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criteria for a…

We consider the capability of $p$-groups of class two and odd prime exponent. The question of capability is shown to be equivalent to a statement about vector spaces and linear transformations, and using the equivalence we give proofs of…

When the standard representation of a crystallographic Coxeter group $\Gamma$ is reduced modulo an odd prime $p$, a finite representation in some orthogonal space over $\mathbb{Z}_p$ is obtained. If $\Gamma$ has a string diagram, the latter…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. We discuss the transformation…

The goal of this paper is to study a $p$-adic analog of the joint of the conjectures of Andr\'e--Oort and Andr\'e--Pink. More precisely, on a product of ordinary Siegel formal moduli schemes, we study the distribution of points whose…